Regrind, Inc. regrinds used typewriter platens. The cost per platen is $1.70. The fixed cost to run the grinding machine is $267 per day. If the company sells the reground platens for $4.70, how many must be reground daily to break even?
4.7 -1.7 = 267
3x = 267
x = 89
To break even, the total cost must equal the total revenue.
Let's assume "x" represents the number of platens that must be reground daily to break even.
The variable costs associated with grinding "x" platens daily would be the cost per platen, which is $1.70 multiplied by "x". So the variable cost is 1.70x.
The fixed cost to run the grinding machine is $267 per day.
The total cost is the sum of the variable cost and the fixed cost. So the total cost is 1.70x + $267.
The revenue generated by selling "x" reground platens would be the selling price per platen, which is $4.70 multiplied by "x". So the revenue is 4.70x.
To break even, the total cost must equal the total revenue. Therefore, the equation becomes:
1.70x + $267 = 4.70x
Now, let's solve for "x":
Subtract 1.70x from both sides:
$267 = 3x
Divide both sides by 3:
x = $267/3
So, to break even, Regrind, Inc. must regrind approximately 89 platens daily.
To determine the number of typewriter platens that must be reground daily to break even, we need to calculate the breakeven point.
The breakeven point is the number of units that need to be sold to cover all costs (both variable and fixed) without making a profit or loss.
First, let's determine the variable cost per platen. The cost per platen is given as $1.70.
Next, let's calculate the contribution margin per platen, which is the selling price minus the variable cost. The selling price is $4.70.
Contribution Margin = Selling Price per Unit - Variable Cost per Unit
Contribution Margin = $4.70 - $1.70
Contribution Margin = $3.00
Now, we can calculate the breakeven point in terms of the number of platens:
Breakeven Point (in units) = Fixed Costs / Contribution Margin
Breakeven Point = $267 / $3.00
Breakeven Point ≈ 89 platens
Therefore, Regrind, Inc. must reground approximately 89 typewriter platens per day to break even.
Cost = Revenue to break even.
267 + 1.70 x = 4.70 x
Solve for x.